feat: implement search functionality with results display, add search input component, and update API for search results

thoughts-frontend/components/search-input.tsx

@@ -0,0 +1,29 @@
+"use client";
+
+import { useRouter } from "next/navigation";
+import { Input } from "./ui/input";
+import { Search as SearchIcon } from "lucide-react";
+
+export function SearchInput() {
+  const router = useRouter();
+
+  const handleSearch = (e: React.FormEvent<HTMLFormElement>) => {
+    e.preventDefault();
+    const formData = new FormData(e.currentTarget);
+    const query = formData.get("q") as string;
+    if (query) {
+      router.push(`/search?q=${encodeURIComponent(query)}`);
+    }
+  };
+
+  return (
+    <form onSubmit={handleSearch} className="relative w-full max-w-sm">
+      <SearchIcon className="absolute left-3 top-1/2 -translate-y-1/2 h-4 w-4 text-muted-foreground" />
+      <Input
+        name="q"
+        placeholder="Search for users or thoughts..."
+        className="pl-9 md:min-w-[250px]"
+      />
+    </form>
+  );
+}